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Izv. Akad. Nauk SSSR Ser. Mat., 1990, Volume 54, Issue 3, Pages 435–468 (Mi izv1081)  

This article is cited in 8 scientific papers (total in 8 papers)

Deforming torison-free sheaves on an algebraic surface

I. V. Artamkin


Abstract: This paper investigates the question of removability of singularities of torsion-free sheaves on algebraic surfaces in the universal deformation and the existence in it of a nonempty open set of locally free sheaves, and describes the tangent cone to the set of sheaves having degree of singularities larger than a given one. These results are used to prove that quasitrivial sheaves $\mathscr F$ on an algebraic surface $X$ with $c_2(\mathscr F)>(r+1)\max(1,p_g(X))$ have a universal deformation whose general sheaf is locally free and stable relative to any ample divisor on $X$, and thereby to find a nonempty component of the moduli space of stable bundles on $X$ with $c_1=0$ and $c_2>\max(1,p_g(X))\cdot(r+1)$ on any algebraic surface.

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English version:
Mathematics of the USSR-Izvestiya, 1991, 36:3, 449–485

Bibliographic databases:

UDC: 512.7
MSC: Primary 14F05; Secondary 14J99
Received: 22.11.1988
Revised: 23.01.1989

Citation: I. V. Artamkin, “Deforming torison-free sheaves on an algebraic surface”, Izv. Akad. Nauk SSSR Ser. Mat., 54:3 (1990), 435–468; Math. USSR-Izv., 36:3 (1991), 449–485

Citation in format AMSBIB
\Bibitem{Art90}
\by I.~V.~Artamkin
\paper Deforming torison-free sheaves on an algebraic surface
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1990
\vol 54
\issue 3
\pages 435--468
\mathnet{http://mi.mathnet.ru/izv1081}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1072690}
\zmath{https://zbmath.org/?q=an:0723.14011|0709.14013}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..36..449A}
\transl
\jour Math. USSR-Izv.
\yr 1991
\vol 36
\issue 3
\pages 449--485
\crossref{https://doi.org/10.1070/IM1991v036n03ABEH002030}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Kuleshov, “Stable bundles on $K3$ surfaces”, Math. USSR-Izv., 36:1 (1991), 223–230  mathnet  crossref  mathscinet  zmath  adsnasa
    2. A. N. Tyurin, “The Weil–Petersson metric on the moduli space of stable vector bundles and sheaves on an algebraic surface”, Math. USSR-Izv., 38:3 (1992), 599–620  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Zhenbo Qin, “Simple sheaves versus stable sheaves on algebraic surfaces”, Math Z, 209:1 (1992), 559  crossref  mathscinet  zmath  isi
    4. Zhenbo Qin, “Moduli of simple rank-2 sheaves onK3-surfaces”, manuscripta math, 79:1 (1993), 253  crossref  mathscinet  zmath  isi
    5. Wei-ping Li, Zhenbo Qin, “On blowup formulae for the S-duality conjecture of Vafa and Witten III: relations with vertex operator algebras”, crll, 2002:542 (2002), 173  crossref  mathscinet  zmath
    6. Björn Andreas, Gottfried Curio, “Extension bundles and the standard model”, J High Energy Phys, 2007:7 (2007), 053  crossref  mathscinet  adsnasa
    7. Björn Andreas, Gottfried Curio, “Spectral bundles and the DRY-Conjecture”, Journal of Geometry and Physics, 62:4 (2012), 800  crossref
    8. Björn Andreas, Gottfried Curio, “On the existence of stable bundles with prescribed Chern classes on Calabi-Yau threefolds”, Journal of Geometry and Physics, 2013  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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